Spectrum of the Dirac Hamiltonian with the mass hedgehog in arbitrary dimension
Bibliographic record
Abstract
It is shown that the square of the Dirac Hamiltonian with the isotropic mass-hedgehog potential in $d$ dimensions is the number operator of fictitious bosons and fermions over $d$ quantum states. This result allows one to obtain the complete spectrum and degeneracies of the Dirac Hamiltonian with the hedgehog mass configuration in any dimension. The result pertains to low-energy states in the core of a general superconducting or insulating vortex in graphene in two dimensions, and in the superconducting vortex at the topological trivial insulator interface in three dimensions, for example. The spectrum in $d=2$ is also understood in terms of the underlying accidental $\mathit{SU}(2)$ symmetry and the supersymmetry of the Hamiltonian.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".